Superconducting Fluctuation and Pseudogap in Disordered Short Coherence Length Superconductor

TL;DR

This paper explores how disorder affects superconducting fluctuations and pseudogap phenomena in short coherence length d-wave superconductors, revealing nanoscale inhomogeneity and enhanced fluctuations contrary to traditional theories.

Contribution

It develops a self-consistent 1-loop theory for inhomogeneous disordered superconductors and demonstrates the localized nature of fluctuations in short coherence length systems.

Findings

Superconducting fluctuations become nanoscale and localized in disordered short coherence length superconductors.

Disorder enhances superconducting fluctuations, contrasting with Abrikosov-Gorkov theory.

Results align with STM, NMR, and transport measurements in high-$T_c$ cuprates.

Abstract

We investigate the role of disorder on the superconducting (SC) fluctuation in short coherence length d-wave superconductors. The particular intetest is focused on the disorder-induced microscopic inhomogeneity of SC fluctuation and its effect on the pseudogap phenomena. We formulate the self-consistent 1-loop order theory for the SC fluctuation in inhomogeneous systems and analyze the disordered $t$-$t'$-$V$ model. The SC correlation function, electronic DOS and the critical temperature are estimated. The SC fluctuation is localized like a nanoscale granular structure when the coherence length is short, namely the transition temperature is high. This is contrasted to the long coherence length superconductors where the order parameter is almost uniform in the microscopic scale. In the former case, the SC fluctuation is enhanced by the disorder in contrast to the Abrikosov-Gorkov theory. These results are consistent with the STM, NMR and transport measurements in high-$T_{\rm c}$ cuprates and illuminate the essential role of the microscopic inhomogeneity. We calculate the spacial dependence of DOS around the single impurity and discuss the consistency with the NMR measurements.